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Vladikavkaz. Mat. Zh., 2015, Volume 17, Number 2, Pages 37–46 (Mi vmj542)  

This article is cited in 2 scientific papers (total in 2 papers)

Niltriangular subalgebras of the Chevalley algebras and their generalizations

V. M. Levchuk, A. V. Litavrin, N. D. Hodyunya, V. V. Tsigankov

Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, Russia

Abstract: We study some problems concerned with ideals and automorphisms of niltriangular subalgebras of classical Lie type Chevalley algebras over a field $K$ and of their non-finitary generalizations and also automorphisms of adjoint group. We characterize (for Lie type $A_{n-1})$ every Lie ideal of algebra $NT(n,K)$ of all niltriangular $n\times n$ matrices by a selection of constants from $K$. When $K=GF(q)$, this gives a combinatorial expression of number of Lie ideals and, for a simple $q$, also the number of normal subgroups in unitriangular group $UT(n,q)$.

Key words: Chevalley algebra, niltriangular subalgebra, non-finitary generalizations, maximal abelian ideals, automorphisms, adjoint group.

Full text: PDF file (278 kB)
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Document Type: Article
UDC: 512.554
Received: 30.04.2015

Citation: V. M. Levchuk, A. V. Litavrin, N. D. Hodyunya, V. V. Tsigankov, “Niltriangular subalgebras of the Chevalley algebras and their generalizations”, Vladikavkaz. Mat. Zh., 17:2 (2015), 37–46

Citation in format AMSBIB
\Bibitem{LevLitHod15}
\by V.~M.~Levchuk, A.~V.~Litavrin, N.~D.~Hodyunya, V.~V.~Tsigankov
\paper Niltriangular subalgebras of the Chevalley algebras and their generalizations
\jour Vladikavkaz. Mat. Zh.
\yr 2015
\vol 17
\issue 2
\pages 37--46
\mathnet{http://mi.mathnet.ru/vmj542}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. M. Levchuk, A. V. Litavrin, “Gipertsentralnye avtomorfizmy niltreugolnykh podalgebr algebr Shevalle”, Sib. elektron. matem. izv., 13 (2016), 467–477  mathnet  crossref
    2. G. P. Egorychev, “Perechislenie sobstvennykh $t$-mernykh podprostranstv prostranstva $V_m$ nad polem $ GF(q)$”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 17 (2016), 12–22  mathnet
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